# Does $C_d$ change with speed? [closed]

In aircraft drag calculations, drag D is computed as $$D = C_D \cdot \frac{1}{2} \rho V^2 \cdot S$$, with $$C_D$$ a dimensionless factor determined by the "streamline shape" of the measured object.

The question is: is $$C_D$$ always completely independent of airspeed? Are there any circumstances within aviation where measured $$C_D$$ values are variable with speed?

The reason for asking was sparked by car aerodynamics: Porsche claims that the rear spoiler

• decreases drag at lower speeds, as the spoiler increases static pressure at the rear window, thereby "pushing" the car forwards more.

• increases drag (and decreases lift) at higher speeds.

This can only be possible if $$C_d$$ is different for different speeds, since cars do not change their angle of attack. Do fixed objects change $$C_d$$ with speeds? Are there any data results from the aviation world that confirm different $$C_D$$ at different speeds?

Or

If wind tunnel test meassured decrease in drag with fixed spoiler at 100km/h,will spoiler decrease drag at all speeds up to 300km/h as well?

• No, Cd doesn't change with velocity. On a plane it would change only with angle of attack. For a car it wouldn't change at all for a given Mach number and Reynolds number. Sep 24 '21 at 19:23
• Independent of your question - I had in mind that the spoiler of Porsches is adaptive. So at low speed they retract it, and at high speed - it gives more downforce (reduces lift on the rear of the car), and produces more stability. That would obviously change the shape of the car... Sep 24 '21 at 21:45
• @Carl Berger, yes it is adaptive, at 205km/h spoiler increase AoA,but my question is if spoiler is fixed and if at 100km/h reduce drag does at all speeds up to 300km/h reduce drag as well? Sep 25 '21 at 0:43
• @stevederekson555 Re changes with speed since car dimensions are constant, and that causes a change in c$_d$ as well. Sep 25 '21 at 9:11
• Please note this site is only for aviation-related questions as described in the help center (Note the caveat "Aerodynamics (related to aircraft)" in the on-topic page). You may like to take a look at Physics which might accept questions like this.
– Jamiec
Sep 28 '21 at 8:22

$$C_D$$ is a form factor variable, constructed to be as independent as possible of all the factors that contribute to aerodynamic forces. Two dimensionless flow parameters do influence outcomes of aerodynamic measurements:

• The Mach number, which quantifies compressibility of air.
• The Reynolds number, which accounts for viscosity/inertia effects in the boundary layer.

On our Aviation Stack, most airflow considerations are relevant to long slender bodies at flight speed (between take-off and cruise speed), meaning the range of Re is reasonably limited. For a car this may be a different matter.

Re can be illustrated with the golf ball effect: the wake around the golf ball without dimples is what happens at lower Re, where viscosity effects dominate. At higher Re the boundary layer becomes turbulent and can follow the contours of the ball better, which creates less pressure drag.

Flight at lower Re takes place in gliders, and there are measurement data on glider airfoils at various Re. For instance in this book, Low Speed Airfoil Data by M. Selig, figure above is from page 68. It clearly shows how $$C_D$$ values change with Re at constant $$C_L$$. Note that differences at higher values are very small, at lower values very large.

This can only be possible if Cd is different for different speeds.

Yes indeed, at lower Re with laminar boundary layer we'll find a different $$C_D$$ than at high Re with mainly turbulent boundary layer.

Cars are short bodies moving entirely in ground effect, and usually the frontal area is used as the reference for $$C_D$$ as the form factor variable. Why? Because short streamline bodies dominant aerodynamic drag factor is the pressure drag, including suction pressure from the separated flow at the rear. And this flow separation takes place only at higher speeds, especially with the gently sloping rear of the Porsche - which reduces drag, but (unfortunately for a car) also produces local lift.

Pics above are from this very comprehensive master's thesis and show how the spoiler usually reduces drag: by reducing turbulence in the wake, thereby increasing the local air pressure. The thesis also mentions Porsche, and the way that OPs referenced spoiler works:

Companies such as Porsche, Bugatti or Mercedes have been using different technologies for spoilers and trying to maximizing the efficiency of it by eliminating the side effects in low speeds and increasing the advantages on high speeds. One of the most commonly used features is to have a hydraulic wing style spoiler at the rear end of vehicle that raises or lower at certain speeds to maintain down force on the backside of vehicle or to create air brake. This feature has been used mostly for safe driving. Spoiler deployment operation is usually automatic. The software operates the spoiler and fixes it in the certain height depends on the vehicle speed but the driver through a button in the cabin can also operate it. For instance, hydraulic spoiler that has been used in Bugatti Veyron comes up at high speeds to hold the car on the road better by creating down force. When the car reaches 220 km/h (140 mph), small hydraulic spoiler deploys from the rear bodywork and a wing extends about a foot. This configuration produces substantial down force, provides up to 330 pounds in front and 440 in the rear [16], which helps holding the car to the road in extreme speeds.

• I'd assume the base line is a certain CD, if i increase the CD, wouldn't it increases drag compared to the base line over the whole range? the shape function remains the same .. Sep 24 '21 at 22:03
• @koyovis, my question is: if spoiler is fixed, does spoiler decrease drag at all speeds up to 300km/h? Sep 25 '21 at 0:46
• Please don't answer non aviation question on aviation. Instead direct users to more appropriate stack exchange sites if you would like to answer them there.
– Jamiec
Sep 28 '21 at 8:20
– Jamiec
Sep 28 '21 at 8:28
• Do NOT change the question to fit your agenda!
– Jamiec
Sep 28 '21 at 8:50

For this answer I have to speculate since I do not have the wind tunnel data which would be needed for a more substantial answer.

Why should adding the spoiler reduce drag at lower speed? The most likely reason is a changed flow separation over the car's rear area. I would expect that flow separates already at some point along the rear window if no spoiler is present. Adding the spoiler reduces the slope of the car and will shift the separation point to the trailing edge of the spoiler. This should indeed raise the pressure over the rear window, thus pushing the car forward.

Why does the spoiler add drag at high speed? The higher Reynolds number at higher speed should delay separation and cause attached flow over the rear window plus a suction peak at the higher curvature below the rear window before the flow separates. Adding the spoiler adds more wetted surface and a downward-directed lift force which will cause its own induced drag. But now the suction peak is avoided and some downforce is added instead. The separation occurs again at the trailing edge of the spoiler, so the separated area is a bit larger than without spoiler.

This small drag reduction is not the reason for the spoiler, though. It is really needed to avoid that suction peak at high speed which will make the car impossible to control, especially in crosswinds. Audi learned this the hard way when the designers first would not accept a spoiler on the Audi TT since that would had destroyed the symmetry of the car's contours. After a couple of crashes the engineers eventually could overrule them.

• So in short, re "Do fixed object change Cd with speeds?", the answer is "Yes, due to changes in flow separation point, which are entirely due to the changed Reynolds number"? Sep 25 '21 at 22:45
• @quietflyer So in short: Yes. Sep 26 '21 at 2:00
• @PeterKampf can post link of Audi problem Sep 26 '21 at 11:16
• @LostincurvedSpace-Time Sorry, I omitted which car that was. Here would be one article about it. It even reduced drag at high speed a bit. Sep 26 '21 at 18:14
• Please don't answer non aviation question on aviation. Instead direct users to more appropriate stack exchange sites if you would like to answer them there.
– Jamiec
Sep 28 '21 at 8:20

The drag coefficient is designed to be a coefficient - and hence be as independent from the flow state as possible.

Yet, the simple cd definition $$c_d = D / (1/2 \rho u^2 \times S)$$ just uses the (incompressible) dynamic head of the incoming airflow as reference pressure. This way effects of viscosity are neglected, as are effects of compressibility. As example, there are the compressibility effects over Mach number, a classic chart would look like this:

To be fair - neglecting compressibility effects up to Mach 0.3 leads to errors below 5%, so for a Porsche at 300 km/h (which isn't far from Mach 0.3), that should be fine.

Yes, if only because Cd changes with the Reynolds number, and –all other things equal– the Reynolds number is a function of the airspeed.

• Effect of Reynolds/Mach changes at usual speeds of a car is negligible. Even for planes it usually isn't considered in simple analyses. Sep 24 '21 at 19:52
• +1: it's true, in normal flight range $C_D$ change with Re is negligible, with cars & gliders it is a different matter though. The answer is a bit brief though. Sep 28 '21 at 7:45